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<p><dfn class="terminology">Variation of Parameters</dfn>The general solution to (<a href="" class="xref" data-knowl="./knowl/eq8_5.html" title="Equation 6.6.2">(6.6.2)</a>) may be written as</p>
<div class="displaymath process-math" data-contains-math-knowls="./knowl/eq8_5.html ./knowl/eq8_6.html">
\begin{equation*}
{\bf x}={\bm \Psi}(t)\, {\bf c},
\end{equation*}
</div>
<p class="continuation">where <span class="process-math">\({\bm \Psi}(t)\)</span> is the fundamental matrix. To find a particular solution, we let</p>
<div class="displaymath process-math" data-contains-math-knowls="./knowl/eq8_5.html ./knowl/eq8_6.html">
\begin{equation}
{\bf x}_1={\bm \Psi}(t)\, {\bf u}(t).\tag{6.6.3}
\end{equation}
</div>
<p class="continuation">We want to determine <span class="process-math">\({\bf u}(t)\)</span> such that (<a href="" class="xref" data-knowl="./knowl/eq8_6.html" title="Equation 6.6.3">(6.6.3)</a>) is a solution.</p>
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